Problem: Simplify; express your answer in exponential form. Assume $z\neq 0, a\neq 0$. $\dfrac{{z^{-4}a^{-1}}}{{z^{3}a^{3}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${z^{-4}a^{-1} = z^{-4}a^{-1}}$ On the left, we have ${z^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${z^{-4} = z^{-4}}$ Apply the ideas above to simplify the equation. $\dfrac{{z^{-4}a^{-1}}}{{z^{3}a^{3}}} = \dfrac{{z^{-4}a^{-1}}}{{z^{3}a^{3}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{-4}a^{-1}}}{{z^{3}a^{3}}} = \dfrac{{z^{-4}}}{{z^{3}}} \cdot \dfrac{{a^{-1}}}{{a^{3}}} = z^{{-4} - {3}} \cdot a^{{-1} - {3}} = z^{-7}a^{-4}$